Umumlashgan teskari Gauss taqsimoti

{2 K_p(\sqrt{ab})} x^{(p-1)} e^{-(ax + b/x)/2}</math>|

  cdf        =|
  mean       =$\operatorname {E} [x]={\frac {{\sqrt {b}}\ K_{p+1}({\sqrt {ab}})}{{\sqrt {a}}\ K_{p}({\sqrt {ab}})}}$
$\operatorname {E} [x^{-1}]={\frac {{\sqrt {a}}\ K_{p+1}({\sqrt {ab}})}{{\sqrt {b}}\ K_{p}({\sqrt {ab}})}}-{\frac {2p}{b}}$
$\operatorname {E} [\ln x]=\ln {\frac {\sqrt {b}}{\sqrt {a}}}+{\frac {\partial }{\partial p}}\ln K_{p}({\sqrt {ab}})$|
  median     =|
  mode       =${\frac {(p-1)+{\sqrt {(p-1)^{2}+ab}}}{a}}$|
  variance   =$\left({\frac {b}{a}}\right)\left[{\frac {K_{p+2}({\sqrt {ab}})}{K_{p}({\sqrt {ab}})}}-\left({\frac {K_{p+1}({\sqrt {ab}})}{K_{p}({\sqrt {ab}})}}\right)^{2}\right]$|
  skewness   =|
  kurtosis   =|
  entropy    =|
  mgf        =$\left({\frac {a}{a-2t}}\right)^{\frac {p}{2}}{\frac {K_{p}({\sqrt {b(a-2t)}})}{K_{p}({\sqrt {ab}})}}$|
  char       =$\left({\frac {a}{a-2it}}\right)^{\frac {p}{2}}{\frac {K_{p}({\sqrt {b(a-2it)}})}{K_{p}({\sqrt {ab}})}}$|
}}

Umumlashgan teskari Gauss taqsimoti (generalized inverse Gaussian distribution, GIG) — probability theory va statisticsda uzluksiz probability distributionlarning uch parametrli oilasi.